Question: Complete the recursive formula of the geometric sequence $10\,,\,6\,,\,3.6\,,\,2.16,...$. $a(1)=$
Answer: The first term is $10$ and the common ratio is $\dfrac35$. ${\times\dfrac35\,\curvearrowright}$ ${\times\dfrac35\,\curvearrowright}$ ${\times\dfrac35\,\curvearrowright}$ $10,$ $6,$ $3.6,$ $2.16,...$ This is the recursive formula of $10\,,\,6\,,\,3.6\,,\,2.16,...$. $\begin{cases} a(1)=10 \\\\ a(n)=a(n-1)\cdot\dfrac35 \end{cases}$